Two fair coins are tossed and someone reasons with Omega=\0,1,2\ heads: “P(one head)=13”. What is the mistake?

The three outcomes are not equally likely; with \HH,HT,TH,TT\ the probability is 12

One must divide by 4, so the right answer is 14

There is no mistake: 13 is correct

One must add the probabilities of 0 and 2 heads, giving 23

Exercise · ZW-CLASSICAL-PROBABILITY-009 · ★★★ Advanced

Two fair coins are tossed and someone reasons with \(\Omega=\{0,1,2\}\) heads: “\(P(\text{one head})=\frac13\)”. What is the mistake?

Choose one option.

Show answer

C. The three outcomes are not equally likely; with \(\{HH,HT,TH,TT\}\) the probability is \(\frac12\)

Explanation

The formula favorable over possible cases requires equally likely outcomes. Here “one head” groups two of the four equally likely sequences: \(\frac24=\frac12\).

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Review the concept: Classical probability

The classical probability \(P(A)\) of an event \(A\), when the sample space \(\Omega\) is finite with equally likely outcomes, is the ratio of favorable to possible outcomes.

\[P(A)=\frac{|A|}{|\Omega|}\]

Two fair coins are tossed and someone reasons with \(\Omega=\{0,1,2\}\) heads: “\(P(\text{one head})=\frac13\)”. What is the mistake?

Explanation

Review the concept: Classical probability

More practice problems: classical probability